1kg mass = 1kg weight?

[isaac]

1kg mass = 1kg weight?
Where's the proof?
If in the gravitational field of the Earth a mass weighs 1 kg (weight), then in the gravitational field of that mass the Earth weighs the same 1 kg (weight)! What is the mass of the Earth, and what is the mass that weighs 1 kg of weight?
The gravitational force is the sum of the forces in those two gravitational fields:
The total gravitational force FG between two gravitational fields is 2 kg (weight).
FG = 1 kg + 1 kg = 2 kg (weight) = 2 * 9.81 N
While our convention for the relationship between weight and mass says:
FG = 1 kg mass * 9.81 kg(m^-1)(s^-2) = 9.81 N = 1 kg weight (free fall - g - relative acceleration!)
Physicists today claim: "1 kg of mass = 1 kg of weight," as if it were some natural law ?!

The above convention was adopted without prior definition of what is mass and what is weight!
The concept of relative and absolute acceleration in the gravitational field is also not defined!
When a mass is at rest (on scale), it is acted upon by an absolute acceleration a!
Absolute acceleration a is equal to half of the relative acceleration g!
FG/2 = 1kg weight * relative acceleration (on scale)
How does the scale weigh 1 kg of weight?
The gravitational force of 2 kg weight is divided into the force of 1 kg weight in the center of gravity of the scale and 1 kg weight of the mass we are weighing!
Therefore, only the relative acceleration g/2 acts on the mass at rest!
Therefore it will be:
m * a = 1 kg (weight)
a = g/2
m * g/2 = 1 kg (weight)
m * g = 2 kg (weight)
that is, our convention for the ratio of mass to weight should be:
m * g/2 = 1 kg (weight)
m/2 * g = 1 kg (weight) = 9.81 N
From here Newton's second law would be (w = weight, m = mass):
w/2 * g = m * g ,
w/2 = m ,
whence the ratio of the actual mass m to the weight w is equal to:
w/m = 2/1 (1 kg of weight = 1/2 kg of mass),(weight and mass are not equal and are not the same!)
therefore Newton's Law of Force should be corrected to F = w/2 * a , if the mass is entered using the weight w. In calculations where mass is calculated, all weights should be divided by two to get the correct masses!
Where is the mistake?